Question

In the following figure, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.

Answer 1

Since, AE || BD and CH is a transversal.

∴ ∠CHE = ∠HCB = 120°  ...(i) [Alternate interior angles]

Now, CH || DF and CD is a transversal.

∴ ∠HCB = ∠CDE  ...[Corresponding angles]

⇒ ∠CDE = 120°  ...(ii) [Using (i)]

Also, AB || DF and BD is a transversal.

∴ ∠ABC + ∠CDE = 180°  ...[Co-interior angles]

⇒ ∠ABC = 180° – 120°  ...[Using (ii)]

= 60°

Thus, ∠ABC = 60° and ∠CDE = 120°